Symplectic geometry of projective structures on surfaces with boundary
Abstract
For oriented surfaces with boundary, we consider the infinite-dimensional deformation space of projective structures on with nondegenerate boundary, up to isotopies fixing the boundary. We show that this space carries a natural symplectic structure, and is a Hamiltonian space for the symplectic groupoid integrating the Adler-Gelfand-Dikii-space of the boundary.
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